Let \(\mathcal {X} \in \mathbb {R}^{n_1\times n_2 \times \ldots \times n_d}\)  be a \(d\) -dimensional tensor. The Tensor Train (TT) decomposition [1]} of a tensor \(\mathcal {X}\)  is computed by
\(\nonumber \mathcal {X}^{i_1i_2\ldots i_d} = \sum _{\alpha _1=1}^{r_1}  \ldots \sum _{\alpha _{d-1}=1}^{r_{d-1}} G_1^{i_1\alpha _1} G_2^{\alpha _1i_2\alpha _2} \ldots G_d^{\alpha _{d-1}i_d}\) 
